The consequence of increasing the money supply is generally an increase in economic activity. This effect can be muted if banks refuse to lend and if firms are reluctant to borrow. However, an increase in the money supply generally leads to an increase in economic activity. This is why central banks try to increase the money supply during times of recession.
When the money supply is increased, banks have more money available to lend. This typically drives down the cost of lending (the interest rates) because a greater supply of a thing (in this case, money to be lent) tends to drive down its price. When interest rates go down, businesses and individuals are more likely to borrow money in order to spend it. If they do so, more economic activity is generated as they spend the money they borrowed.
This effect can be reduced if banks and/or borrowers are reluctant. The government cannot force banks to lend or companies to borrow. If banks fear default by borrowers, and if borrowers fear that they cannot afford to borrow, borrowing will not increase much and neither will economic activity.
In general, though, we can expect more economic activity when the money supply increases.